Stationary Higher Spin Six Vertex Model and $q$-Whittaker measure

Understand

In this paper we consider the Higher Spin Six Vertex Model on the lattice $\mathbb{Z}_{\geq 2} \times \mathbb{Z}_{\geq 1}$.

• We first identify a family of translation invariant measures and subsequently we study the one point distribution of the height function for the model with certain random boundary conditions.
• Exact formulas we obtain prove to be useful in order to establish the asymptotic of the height distribution in the long space-time limit for the stationary Higher Spin Six Vertex Model.
• In particular, along the characteristic line we recover Baik-Rains fluctuations with size of characteristic exponent $1/3$.